What is the inverse of the function $h(x)=\dfrac{5}{2}x+4$ ? $h^{-1}(x)=$
Answer: Let's start by replacing $h(x)$ with $y$. $y=\dfrac{5}{2}x+4$ If a function contains the point $(a,b)$, the inverse of that function contains the point $(b,a)$. So if we swap the position of $x$ and $y$ in the equation, we get the inverse relationship. In this case, the function is $y=\dfrac{5}{2}x+4$, so the inverse relationship is $x=\dfrac{5}{2}y+4$. Solving this equation for $y$ will give us an expression for $h^{-1}(x)$. $\begin{aligned} x&=\dfrac{5}{2}y+4\\\\ x-4&=\dfrac{5}{2}y\\\\ \dfrac{2}{5}(x-4)&=y\\\\\\ \end{aligned}$ The inverse of the function is $h^{-1}(x)=\dfrac{2}{5}(x-4)$. [I saw someone solve this problem by originally solving for x. Were they wrong?]